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Math Help - limit of f(x,y) as x,y -> (0,0)

  1. #1
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    limit of f(x,y) as x,y -> (0,0)

    lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
    x,y go to (0,0)

    this limit does not exist and to prove that you must take the limit using two different directions and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?
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    Hello,
    Quote Originally Posted by hharalso View Post
    lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
    x,y go to (0,0)

    this limit does not exist and to prove that you must take the limit using two different directions (and such that they are different) and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?
    Well, the first limit is 0 and the second limit is 1/2
    .
    So you've just proved that the limit doesn't exist !
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  3. #3
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    Quote Originally Posted by hharalso View Post
    lim f(x,y) (x^4y^4)/(x^2 + y^4)^3
    x,y go to (0,0)

    this limit does not exist and to prove that you must take the limit using two different directions and I did one limit on the x-axis y=0 and the limit is 0. Now i must use the equation y=x^1/2 and i can't find the limit of this equation i keep on getting lim=1/2. can someone help me please?
    Are you sure that the limit is 1/2? It looks like 1/2^3 = 1/8 to me.
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